Scanning optical apparatus and image forming apparatus using the same

ABSTRACT

An object of the present invention is to provide a scanning optical apparatus that is capable of suppressing, to a minute amount, scanning line bending caused by rotational decentration of a single lens that is a scanning optical system, and to provide an image forming apparatus using the optical scanning apparatus. To achieve the stated object, with the technique of the present invention, a single lens is used as a scanning optical system and the surface shape of the single lens is set so that a direction of scanning line bending in the sub scanning direction occurring when an incident surface of the single lens is rotationally decenter about an axis parallel to the main scanning direction is opposite to a direction of scanning line bending in the sub scanning direction occurring when an exit surface is rotationally decenter about the axis parallel to the main scanning direction.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a scanning optical apparatus andan image forming apparatus using the scanning optical apparatus. Moreparticularly, the present invention relates to a scanning opticalapparatus that is suitably used for an apparatus, such as a laser beamprinter or a digital copying machine having an electrophotographicprocess, in which an optically modulated light flux emitted from a lightsource means is reflected and deflected by a polygon mirror functioningas an optical deflection means and then optically scans a surface to bescanned through an scanning optical system, thereby recording imageinformation. In particular, the present invention relates to a scanningoptical apparatus with which there is always obtained a favorable imagewhere the sensitivity of scanning line bending to rotationaldecentration of a single lens constituting a scanning optical system isreduced. The present invention also relates to an image formingapparatus using the scanning optical apparatus.

[0003] Also, the present invention relates to a color image formingapparatus that uses a plurality of scanning optical apparatuses and isconstructed from a plurality of image bearing members corresponding torespective colors.

[0004] 2. Related Background Art

[0005] In a conventional scanning optical apparatus applied to a laserbeam printer (LBP) or the like, a light flux optically modulated inaccordance with an image signal and emitted from a light source means isperiodically deflected by a light deflector composed of a rotary polygonmirror (polygon mirror) or the like. The deflected light flux isconverged to form a spot on a surface of a photosensitive recordingmedium (photosensitive drum) by an imaging scanning optical systemhaving an fθ characteristic and optically scans the surface, therebyperforming image recording.

[0006]FIG. 20 is a schematic diagram showing the main part of aconventional scanning optical apparatus.

[0007] In this drawing, a diverging light flux emitted from a lightsource means 171 is converted into a nearly parallel light flux by acollimator lens 172, an aperture stop 173 limits the light flux, and thelimited light flux strikes a cylindrical lens 174 having a predeterminedrefractive power only in the sub scanning direction. The nearly parallellight flux striking the cylindrical lens 174 is emitted as it is in amain scanning cross-section. Also, in a sub scanning cross-section, thelight flux is converged and imaged as a nearly linear image on adeflecting surface (a reflecting surface) 175 a of a light deflector (adeflection means) 175 composed of a polygon mirror.

[0008] Then, the light flux deflected by the deflecting surface 175 a ofthe light deflector (the deflection means) 175 is guided by an imagingscanning optical system 76 having an fθ characteristic onto aphotosensitive drum surface 178 that is a surface to be scanned. Byhaving the light deflector (the deflection means) 175 rotate in thedirection of arrow A, the photosensitive drum surface 178 is opticallyscanned in the direction of arrow B, thereby performing the recording ofimage information.

[0009] In order to perform the recording of image information with highprecision in a scanning optical apparatus like this, it is required thatthe following requirements are met. For instance, the curvature of fieldis favorably corrected across the entire of the surface to be scanned.Also, there exists a distortion characteristic (fθ characteristic)having a uniform speed property between an angle of view θ and an imageheight Y. Further, the spot diameter on an image surface remains uniformirrespective of differences in image height. There have conventionallybeen proposed various kinds of scanning optical apparatuses or imagingscanning optical systems that satisfy optical characteristics likethese.

[0010] On the other hand, as the sizes and prices of apparatuses, suchas laser beam printers and digital copying machines, are reduced, thesame demand is made to scanning optical apparatuses.

[0011] As a construction satisfying the demand like this, JP 04-50908 Aand JP 09-33850 A, for instance, propose a scanning optical apparatuswhose imaging scanning optical system is constructed from a single fθlens.

[0012] In JP 04-50908 A, an aberration characteristic is relativelyfavorably corrected by using an aspheric surface of a high order in themain scanning direction of an fθ lens. However, the magnificationbetween a deflection means and a surface to be scanned in the subscanning direction does not remain constant, so that there is a tendencyfor a spot diameter in the sub scanning direction to change inaccordance with the differences in image height.

[0013] On the other hand, in JP 09-33850 A, there is proposed a methoddescribed below. In a scanning optical apparatus, on at least twosurfaces of lens surfaces of an fθ lens, the curvature in the subscanning direction continuously changes along the main scanningdirection within an effective region of the fθ lens as well asindependently of the curvature in the main scanning direction. With thismethod, the position of the principal plane in the sub scanningdirection is controlled by the bending of two surfaces. In this manner,the sub scanning magnification is kept constant irrespective of thedifferences in image height, so that there is obtained a constant spotdiameter.

[0014] With the proposed method described above, in order to obtain aconstant sub scanning magnification, at least two surfaces are bent andthe position of the principal plane is controlled so that themagnification is kept constant. Consequently, it becomes possible to setshapes in the main scanning direction and the sub scanning directioncompletely independently of each other. However, because of variousdemands such as a demand to reduce the thickness of a lens, the lensshape in the main scanning direction has a relatively large amount of anaspheric surface in many cases.

[0015] In a lens like this whose amount of an aspheric surface in themain scanning direction is large, optical performance is significantlydegraded due to errors caused during the arrangement of each lenssurface and the lens. Among the degradations of optical performance, asdistinct from the aberration of the height of a scanning line, theinclination of the scanning line, and the like, the bending of thescanning line in the sub scanning direction in particular causes asignificant problem because it is impossible to correct this bending bythe adjustment of a mirror or the like arranged in an apparatus mainbody. Consequently, in order to suppress the scanning line bending to aminute amount, it is required to precisely arrange each lens surface andthe lens in accordance with design values or to adjust the positions ofeach lens surface and the lens so as to coincide with design positionsby providing the lens with an adjustment mechanism.

[0016] Further, in the case of a color image forming apparatus in whichscanning optical apparatuses are arranged using four photosensitivemembers (photosensitive drums), latent images are formed by laser light,and images on an original in respective colors of Y (yellow), M(magenta), C (cyan), and Bk (black) are formed on the surfaces of theircorresponding photosensitive members, images in four colors of Y, M, C,and Bk formed on the surfaces of respective photosensitive members aresuperimposed on each other on a transfer member such as paper.Consequently, if the scanning lines of the scanning optical apparatusescorresponding to respective photosensitive members are bent, there occurdifferences in shape between scanning lines for the four colors, whichcauses a problem that color drift occurs in an image on the transfermember and therefore image performance is significantly degraded.

SUMMARY OF THE INVENTION

[0017] The present invention has been made to solve these problems andan object of the present invention is to provide a scanning opticalapparatus that is capable of suppressing scanning line bending caused byrotational decenterity of a single lens to a minute amount and an imageforming apparatus using the scanning optical apparatus. To do so, an fθlens is constructed using a single lens and the shape of the fθ lens isappropriately set so that there are favorably corrected the fieldcurvature characteristic that is a characteristic of an optical system,an fθ characteristic for performing uniform speed scanning, and wavefront aberration.

[0018] According to a first aspect of the present invention, there isprovided a scanning optical apparatus comprising: light source means;deflection means for deflecting a light flux emitted from the lightsource means; and a scanning optical system that images the deflectedlight flux as a spot on a surface to be scanned, in which the scanningoptical system is a single lens, and a surface shape of the single lensis set so that a direction of scanning line bending in a sub scanningdirection occurring when an incident surface of the single lens isrotationally decenter about an axis parallel to a main scanningdirection is opposite to a direction of scanning line bending in the subscanning direction occurring when an exit surface of the single lens isrotationally decenter about the axis parallel to the main scanningdirection.

[0019] According to a second aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, the scanning line bending in the sub scanning directionoccurring when the incident surface of the single lens is rotationallydecenter about the axis parallel to the main scanning direction cancelsout the scanning line bending in the sub scanning direction occurringwhen the exit surface of the single lens is rotationally decenter aboutthe axis parallel to the main scanning direction.

[0020] According to a third aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, when power in the sub scanning direction of entirety of thescanning optical system is referred to as Φs and power in the subscanning direction of the exit surface of the single lens is referred toas Φs2, the power in the sub scanning direction of the exit surface ofthe single lens satisfies a condition of 0.9 Φs2/Φs 1.1.

[0021] According to a fourth aspect of the present invention, in thefirst aspect of the invention, there is provided a scanning opticalapparatus, in which power in the sub scanning direction of an exitsurface of the single lens satisfies a condition of 0.95 Φs2/Φs 1.05.

[0022] According to a fifth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, when an air converted distance from the deflection means tothe exit surface of the single lens on an optical axis is referred to asLao, a distance from the exit surface of the single lens to the surfaceto be scanned is referred to as L_(bo), an off-axis air converteddistance from the deflection means to the exit surface of the singlelens is referred to as L_(aθ), and a distance from the exit surface ofthe single lens to the surface to be scanned is referred to as L_(bθ), ashape of the exit surface of the single lens in the main scanningdirection satisfies the following condition:${0.9 \times \frac{L_{bo}}{L_{ao}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.1\frac{L_{bo}}{L_{ao}}}$

[0023] According to a sixth aspect of the present invention, in theoptical scanning apparatus according to the fourth aspect of theinvention, a shape of the exit surface of the single lens in the mainscanning direction satisfies the following condition.

[0024] According to a seventh aspect of the present invention, in thescanning optical apparatus according to the first aspect of theinvention, a light flux forming a linear image that is long in the mainscanning direction is incident on the deflection means.

[0025] According to an eighth aspect of the present invention, in thescanning optical apparatus according to the first aspect of theinvention, the single lens is formed by a molding process.

[0026] According to a ninth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, at least one of power of the exit surface in the sub scanningdirection and power of the incident surface in the sub scanningdirection varies without any correlation with a shape in the mainscanning direction.

[0027] According to a tenth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, a radius of curvature of the exit surface in the sub scanningdirection varies from on the axis toward off the axis.

[0028] According to an eleventh aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, each of the incident surface and the exit surface is ananamorphotic surface.

[0029] According to a twelfth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, a shape of the exit surface of the single lens is circulararc.

[0030] According to a thirteenth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, a shape of the exit surface of the single lens isnon-circular arc.

[0031] According to a fourteenth aspect of the present invention, in theoptical scanning apparatus according to the first aspect of theinvention, a difference between imaging magnifications in the subscanning direction of the scanning optical system within an imageeffective area is 10% or less.

[0032] According to a fifteenth aspect of the present invention, in thescanning optical apparatus according to the twelfth aspect of theinvention, a shape of the exit surface of the single lens in the mainscanning direction is a nearly circular arc shape having a center ofcurvature on the deflection means side.

[0033] According to a sixteenth aspect of the present invention, in thescanning optical apparatus according to the first aspect of theinvention, the single lens satisfies the following equations:$\begin{matrix}{{{\Delta \quad Z_{1}}} = {{{{\Delta \quad Z_{1d}} + {\Delta \quad Z_{1L}} + {\Delta \quad Z_{1\varphi}} + {\Delta \quad Z_{2}}}} \leq 0.040}} \\{{\Delta \quad Z_{2}} = {\Delta \quad X_{2} \times \frac{L_{2o}}{{fs}_{2o}} \times \gamma}} \\{{\Delta \quad Z_{1d}} = {\frac{N - 1}{N} \times \frac{1}{\cos^{2}\varphi} \times \left( {1 - \frac{L_{2o}}{{fs}_{2o}}} \right) \times \gamma \times \left( {d_{\theta} - d_{o}} \right)}} \\{{\Delta \quad Z_{1L}} = {\left( {N - 1} \right) \times \frac{1}{\cos^{2}\varphi} \times \gamma \times \left( {L_{2\theta} - L_{2o}} \right)}} \\{{\Delta \quad Z_{1\varphi}} = {\left( {N - 1} \right) \times L_{2o} \times \gamma \times \tan^{2}\varphi}}\end{matrix}$

[0034] where ΔX₂ is a deviation of an exit surface 6 b of the lens,

[0035] Rx_(o) is a distance from the exit surface of the lens to acenter of sagittal curvature on an optical axis along a direction of theoptical axis,

[0036] Rx_(θ) is a distance from the exit surface of the lens to thecenter of sagittal curvature at an angle of view θ along the directionof the optical axis,

[0037] L_(2o) is a distance from the exit surface of the lens to thesurface to be scanned on the optical axis,

[0038] L2θ is a distance from the exit surface of the lens to thesurface to be scanned at an angle of view

[0039] fs_(2o) is a focal length of the exit surface of the lens in thesub scanning direction on the optical axis,

[0040] fs_(2o) is a focal length of the exit surface of the lens in thesub scanning direction at the angle of view θ,

[0041] N is a refractive index of the lens,

[0042] d_(o) is a distance between the incident surface and the exitsurface of the lens on the optical axis,

[0043] d_(θ) is a distance between an incident surface 6 a and the exitsurface of a lens 6 at the angle of view θ,

[0044] fs_(2o) is a focal length of the exit surface of the lens in thesub scanning direction on the optical axis,

[0045] fs_(2θ) is a focal length of the exit surface of the lens in thesub scanning direction at the angle of view θ,

[0046] L_(2o) is a distance from the exit surface of the lens to thesurface to be scanned on the optical axis,

[0047] L_(2θ) is a distance from the exit surface of the lens to thesurface to be scanned at the angle of view θ, and

[0048] Φis an inclination of a ray of light after emission from theincident surface in the main scanning direction at the angle of view θ.

[0049] According to a seventeenth aspect of the present invention, inthe scanning optical apparatus according to the first aspect of theinvention, the light source means is a multi-beam light source having aplurality of light-emitting points that can be modulated independentlyof each other.

[0050] According to an eighteenth aspect of the present invention, thereis provided an image forming apparatus comprising: a scanning opticalapparatus according to any one of the first to seventeenth aspects ofthe invention; a photosensitive member arranged on the surface to bescanned; a developing device that develops an electrostatic latent imageformed on the photosensitive member by a light flux scanned by thescanning optical apparatus as a toner image; a transferring device thattransfers the developed toner image onto a material to be transferred;and a fixing device that fixes the transferred toner image on thematerial to be transferred.

[0051] According to a nineteenth aspect of the present invention, thereis provided an image forming apparatus comprising: a scanning opticalapparatus according to any one of the first to seventeenth aspects ofthe invention; and a printer controller that converts code data inputtedfrom an external device into an image signal and inputs the image signalinto the scanning optical apparatus.

[0052] According to a twentieth aspect of the present invention, thereis provided an image forming apparatus comprising: a plurality ofscanning optical apparatuses that are each a scanning optical apparatusaccording to any one of the first to seventeenth aspects of theinvention; and a plurality of image bearing members that are arranged onsurfaces to be scanned of respective scanning optical apparatuses andform images in colors differing from each other.

BRIEF DESCRIPTION OF THE DRAWINGS

[0053]FIGS. 1A and 1B are a main scanning cross-sectional view and a subscanning cross-sectional view in a first embodiment of the presentinvention;

[0054]FIG. 2 is a schematic diagram showing the main part in the firstembodiment of the present invention;

[0055]FIG. 3 shows design data in the first embodiment of the presentinvention;

[0056]FIGS. 4A, 4B, and 4C are aberration diagrams in the firstembodiment of the present invention;

[0057]FIG. 5 shows the distance of a scanning line in the firstembodiment of the present invention;

[0058]FIG. 6 also shows the distance of a scanning line in the firstembodiment of the present invention;

[0059]FIGS. 7A and 7B are a main scanning cross-sectional view and a subscanning cross-sectional view in a second embodiment of the presentinvention;

[0060]FIG. 8 is a schematic diagram showing the main part of a colorimage forming apparatus in the second embodiment of the presentinvention;

[0061]FIG. 9 shows design data in the second embodiment of the presentinvention;

[0062]FIGS. 10A, 10B, and 10C are aberration diagrams in the secondembodiment of the present invention;

[0063]FIG. 11 shows the distance of a scanning line in the secondembodiment of the present invention;

[0064]FIG. 12 also shows the distance of a scanning line in the secondembodiment of the present invention;

[0065]FIGS. 13A and 13B are a main scanning cross-sectional view and asub scanning cross-sectional view in a third embodiment of the presentinvention;

[0066]FIG. 14 shows design data in the third embodiment of the presentinvention;

[0067]FIGS. 15A, 15B, and 15C are aberration diagrams in the thirdembodiment of the present invention;

[0068]FIG. 16 shows the distance of a scanning line in the thirdembodiment of the present invention;

[0069]FIG. 17 also shows the distance of a scanning line in the thirdembodiment of the present invention;

[0070]FIG. 18 is a schematic diagram showing the main part of an imageforming apparatus of the present invention;

[0071]FIG. 19 is a schematic diagram showing the main part of a colorimage forming apparatus of the present invention; and

[0072]FIG. 20 is a perspective view of a conventional scanning opticalapparatus.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0073] First Embodiment

[0074]FIG. 1A is a main scanning cross-sectional view of a scanningoptical apparatus in a first embodiment of the present invention, whileFIG. 1B is a sub scanning cross-sectional view thereof.

[0075] Here, the main scanning direction means a direction in which alight flux is scanned by optical scanning, while the sub scanningdirection means a direction orthogonal to an optical axis and the mainscanning direction.

[0076] Diverging light from a semiconductor laser 1 that is a lightsource means is converted into a nearly parallel light flux by a singlecollimator lens 2 constituting a first optical system. Following this,the width of the light flux is limited by an aperture stop 3 to obtain adesired spot diameter.

[0077] A second optical system is constructed from a single cylindricallens 4 having a predetermined refractive power only in the sub scanningdirection. The light flux is imaged as a linear image, which is long inthe main scanning direction, in the vicinity of a deflecting surface 5 aof a deflection means 5 to be described later.

[0078] Reference numeral 5 denotes the deflection means that isconstructed, for instance, from a polygon mirror (rotary polygon mirror)having a four-surface construction. This deflection means is rotated ata constant speed in the direction of arrow A in the drawing by a drivingmeans (not shown) like a motor.

[0079] Reference numeral 61 represents a third optical system (scanningoptical system) having an fθ characteristic. This third optical systemallows a light flux reflected and deflected by the deflection means 5 tobe imaged on a photosensitive member drum surface 7 functioning as asurface to be scanned. The third optical system also corrects thesurface inclination of the deflecting surface 5 a of the deflectionmeans 5. During this correction, two light fluxes reflected anddeflected by the deflecting surface 5 a of the deflection means areguided onto the photosensitive member drum surface 7 through the thirdoptical system 61 and simultaneously optical scanning is performed onthe photosensitive member drum surface 7 in the direction of arrow B byhaving the polygon mirror 5 rotate in the direction of arrow A. By doingso, a scanning line is formed on the photosensitive member drum surfaceand image recording is performed.

[0080] Here, there will be described a single fθ lens constituting thethird optical system (imaging scanning optical system) 61.

[0081] The fθ lens 61 is a plastic lens formed by a molding process fromZEONEX E48R (manufactured by ZEON Corporation) that is an optical resin.Only an exit surface 61 b of this lens has power (refractive power) inthe sub scanning direction. In addition, the shape in the main scanningdirection (meridional shape) is a circular arc shape whose center ofcurvature exists on the polygon mirror 5 side and which allows the subscanning magnification to be kept approximately constant.

[0082] Here, as shown in FIG. 2, the main scanning direction shape(meridional shape), with which the sub-scanning magnification is keptconstant, is a shape where the ratio between (1) an air converteddistance (conversion for the inside of the lens is performed by dividingan actual distance by a refractive index) from the deflecting surface 5a of the polygon mirror 5 to the exit surface 61 b of the scanning lens61 and (2) a distance from the exit surface 61 b to the surface to bescanned 7 is kept approximately constant within an image effective area.As a result, the main scanning direction shape becomes a nearly circulararc shape whose center of curvature exists on the polygon mirror 5 side.The ratio is expressed as follows:

[0083] $\left( {\frac{M2}{M1} \simeq \frac{P2}{P1}} \right)$

[0084] Also, there is obtained a shape where only the exit surface 61 bhas power in the sub scanning direction and the radius of curvaturegradually increases from an optical axis toward off the axis. With thisshape, there are corrected the curvature of field in the sub scanningdirection and the uniformity of the sub scanning magnification (constantsub scanning magnification).

[0085] In the main scanning direction, the shape of the exit surface 61b is a circular arc shape, with which there is obtained a constant subscanning magnification, and the incident plane 61 a has a non-circulararc shape with which there are corrected the remaining curvature offield in the main scanning direction and an fθ characteristic.

[0086]FIG. 3 shows design data in this embodiment.

[0087] The surface shape of the refracting surface of the presentinvention is expressed by the following shape expressing equation.

[0088] When the intersection point with the optical axis is set as anorigin, the optical axis direction is set as an X axis, an axisorthogonal to the optical axis within the main scanning plane is set asa Y axis, and an axis orthogonal to the optical axis within the subscanning plane is set as a Z axis, the meridional directioncorresponding to the main scanning direction is obtained from thefollowing equation.$X = {\frac{Y^{2}/R}{1 + \sqrt{1 - {\left( {1 + k} \right)\left( \frac{Y}{R} \right)^{2}}}} + {B_{4}Y^{4}} + {B_{6}Y^{6}} + {B_{8}Y^{8}} + {B_{10}Y^{10}}}$

[0089] (where R is the radius of curvature and k, B₄, B₆, B₈, and B₁₀are each an aspheric surface coefficient)

[0090] Also, the sagittal direction corresponding to the sub scanningdirection (direction including the optical axis and orthogonal to themain scanning direction) is obtained from the following equation.$S = \frac{Z^{2}/r^{\prime}}{1 + \sqrt{1 - \left( {Z/r^{\prime}} \right)^{2}}}$r^(′) = r₀(1 + D₂Y² + D₄Y⁴ + D₆Y⁶ + D₈Y⁸ + D₁₀Y¹⁰)

[0091] (where r′ is the radius of curvature of the sagittal line on theoptical axis and D₂, D₄, D₆, D₈, and D₁₀ are each a coefficient)

[0092] It should be noted here that the radius of curvature of thesagittal line r′ off the optical axis is defined within a planeincluding the normal of the meridional line at each position andperpendicular to the main scanning surface. Also, the polynomialexpression in the shape expressing equation is expressed using afunction of up to the 10th order, although there occurs no problem evenif the order is higher or lower than this.

[0093] Also, FIGS. 4A to 4C are aberration diagrams of the scanningoptical apparatus in this embodiment.

[0094] As can be seen from these drawings, the curvatures of field inboth of the main scanning direction and the sub scanning direction areat or below ±0.5 mm and the uniformity of the sub-scanning magnificationis at or below 2.5%, which means that correction is favorably performed.It is required that from the viewpoint of practical use as a scanningoptical apparatus, the magnification difference in the sub scanningdirection within an image effective area is suppressed to 10% or lower,or preferably to 5% or lower.

[0095] When doing so, with the construction where a constant subscanning magnification within an image effective area is obtained likethe single fθ lens 61 of this embodiment, in the case where the whole ofthe scanning lens 6 is decenter in the sub scanning direction (Zdirection) due to errors caused during the attachment of the lens to anoptical box (case) and errors caused during the manufacturing of thelens itself, a scanning line is shifted in its entirety, which makes itpossible to avoid the bending of the scanning line.

[0096] Also, the single fθ lens 61 of this embodiment has a constructionwhere the incident surface 61 a has no power in the sub scanningdirection and only the exit surface 61 b has power, so that the subscanning magnification is kept constant across each of the incidentsurface 61 a and the exit surface 61 b of the single fθ lens 61.

[0097] With this construction, in particular, even in the case wherethere occurs decentration of the exit surface 61 b with reference to theincident surface 61a in the sub scanning direction due to theinsufficient attachment accuracy within a mold used for a molded lens,the scanning line is shifted in its entirety, which makes it possible toavoid the bending of the scanning line.

[0098] Following this, there will be described the bending of a scanningline in the case where rotational decentration occurs to the incidentsurface 61 a and the exit surface 61 b of the single fθ lens 61 about anaxis parallel to the main scanning direction.

[0099] In the case where the exit surface 61 b is rotationally decenterby an angle of rotation γ about the axis parallel to the main scanningdirection, when the height of a ray of light on an optical axis reachingthe surface to be scanned is referred to as Z_(2o) and the height of aray of light with an angle of view θ reaching the surface to be scanned7 is referred to as Z_(2θ), it is possible to calculate the bendingamount ΔZ₂ of the scanning line from the following equations.

ΔZ ₂ =Z _(2θ) −Z _(2o)  (1)

[0100] $\begin{matrix}{Z_{2o} = {{Rx}_{o} \times \frac{L_{2o}}{{fs}_{2o}} \times \gamma}} & (2) \\{Z_{2\theta} = {\left( {{\Delta \quad X_{2}} + {Rx}_{\theta}} \right) \times \frac{L_{2\theta}}{{fs}_{2\theta}} \times \gamma}} & (3)\end{matrix}$

[0101] where ΔX₂ is a deviation of the lens exit surface 6 b,

[0102] Rx_(o) is a distance from the exit surface 6 b of the lens to acenter of sagittal curvature on an optical axis along a direction of theoptical axis,

[0103] Rx₇₄ is a distance from the exit surface 6 b of the lens to thecenter of sagittal curvature at an angle of view θ along the directionof the optical axis,

[0104] L_(2o) is a distance from the exit surface 6 b of the lens to thesurface to be scanned on the optical axis,

[0105] L_(2θ) is a distance from the exit surface 6 b of the lens to thesurface to be scanned at an angle of view θ,

[0106] fs_(2o) is a focal length of the exit surface 6 b of the lens inthe sub scanning direction on the optical axis,

[0107] fs_(2θ) is a focal length of the exit surface 6 b of the lens inthe sub scanning direction at the angle of view θ,

[0108] Here, the deviation means a sag amount in the optical axisdirection with reference to a lens surface position on the optical axisat the lens surface position. Also, in this embodiment, the sagittalline is formed in a direction perpendicular to the meridional line, sothat R_(xθ) is calculated from the following equation by applying anangle of inclination η of the meridional line to the radius of curvatureR_(sθ) of the sagittal line at an exit surface position of the lens.

Rx _(θ) =Rsθ×cos η  (4)

[0109] Also, in the case where the incident surface 61 a is rotationallydecenter by an angle of rotation γ about the axis parallel to the mainscanning direction, when the height of a ray of light on an optical axisreaching the surface to be scanned is referred to as Z_(1o) and theheight of a ray of light with an angle of view θ reaching the surface tobe scanned 7 is referred to as Z_(1θ), it is possible to calculate thebending amount ΔZ₁ of the scanning line from the following equations.

ΔZ ₁ =Z _(1θ) −Z _(1o)  (5)

[0110] $\begin{matrix}{Z_{1o} = {\frac{N - 1}{N} \times d_{o} \times \left\{ {{\left( {\frac{N}{d_{o}} - \frac{1}{{fs}_{2o}}} \right) \times L_{2o}} + 1} \right\} \times \gamma}} & (6) \\{Z_{1\theta} = {\frac{N - 1}{N} \times d_{\theta} \times \left\{ {{\left( {\frac{N}{d_{\theta}} - \frac{1}{{fs}_{2\theta}}} \right) \times L_{2\theta}} + 1} \right\} \times \frac{1}{\cos^{2}\varphi} \times \gamma}} & (7)\end{matrix}$

[0111] where N is a refractive index of the scanning lens 61,

[0112] d_(o) is a distance between the incident surface 61 a and theexit surface 61 b of the fθ lens 61 on the optical axis,

[0113] d_(θ) is a distance between the incident surface 61 a and theexit surface 61 b of the fθ lens 61 at the angle of view θ,

[0114] fs_(2o) is a focal length of the exit surface 61 b of the lens inthe sub scanning direction on the optical axis,

[0115] fs2θ is a focal length of the exit surface 61 b of the lens inthe sub scanning direction at the angle of view θ,

[0116] L_(2o) is a distance from the exit surface 61 b of the lens tothe surface to be scanned 7 on the optical axis,

[0117] L_(2θ) is a distance from the exit surface 61 b of the lens tothe surface to be scanned 7 at the angle of view θ, and

[0118] Φ is an inclination of a ray of light after emission from theincident surface 61 a in the main scanning direction at the angle ofview θ.

[0119] It is possible to obtain the amount of the scanning line bendingΔZ₁ in the case where the single fθ lens 61 is rotationally decenterabout the axis parallel to the main scanning direction as the sum of theamount of the scanning line bending occurring on the incident surface 61a and the amount of the scanning line bending occurring on the exitsurface 61 b.

ΔZ ₁ =ΔZ ₁ +ΔZ ₂  (8)

[0120] Here, there will be described a method of approximately obtainingthe scanning line bending amount.

[0121] In this embodiment, the power in the sub scanning direction isconcentrated on the exit surface 61 b and the sub scanning magnificationis kept constant, so that a ratio L2/fs2 between a distance L from theexit surface 61 b to the surface to be scanned and a focal length fs2 ofthe exit surface 61 b in the sub scanning direction assumes a constantvalue irrespective of the angle of view θ. As a result, a value ofL2o/fs2o on the optical axis is applied to all angles of view as arepresentative.

[0122] Also, there exists the following relation.

ΔX ₂ >>Rx ₂ −Rx _(o)  (9)

[0123] As a result, it becomes possible to delete the component of Rx(distance from the exit surface 61 b of the lens to the center ofcurvature of the sagittal line along the optical axis direction).

[0124] Consequently, the sole parameter varying between on the opticalaxis and the angle of view θ (factor causing the scanning line bending)is ΔX₂. As a result, it becomes possible to calculate the scanning linebending amount ΔZ₂ in the case where the exit surface 61 b isrotationally decenter by the angle of rotation γ about the axis parallelto the main scanning direction from a simple equation given below.$\begin{matrix}{{\Delta \quad Z_{2}} = {\Delta \quad X_{2} \times \frac{L_{2o}}{{fs}_{2o}} \times \gamma}} & (10)\end{matrix}$

[0125] Also, as to the scanning line bending amount ΔZ₁ in the casewhere the incident surface 61 a is rotationally decenter about the axisparallel to the main scanning direction, there exist three parametersvarying between on the optical axis and the angle of view θ (factorscausing the scanning line bending). The parameters are d (distancebetween the incident surface 61 a and the exit surface 61 b of the fθlens 61), L₂ (distance from the lens exit surface 61 b to the surface tobe scanned 7), and Φ (inclination of a ray of light after the outgoingfrom the incident surface 61 a in the main scanning direction).

[0126] In view of this situation, the amount of the scanning linebending to be caused is calculated for each parameter and the sumthereof is set as the scanning line bending amount occurring when the fθlens is rotationally decenter about the axis parallel to the mainscanning direction.

[0127] Also, each scanning line bending amount becomes as expressed bythe following equations.

ΔZ ₁ =ΔZ _(1d) +ΔZ _(1L) ΔZ _(1Φ)  (11)

[0128] $\begin{matrix}{{\Delta \quad Z_{1d}} = {\frac{N - 1}{N} \times \frac{1}{\cos^{2}\varphi} \times \left( {1 - \frac{L_{2o}}{{fs}_{2o}}} \right) \times \gamma \times \left( {d_{\theta} - d_{o}} \right)}} & (12) \\{{\Delta \quad Z_{1L}} = {\left( {N - 1} \right) \times \frac{1}{\cos^{2}\varphi} \times \gamma \times \left( {L_{2\theta} - L_{2o}} \right)}} & (13) \\{{\Delta \quad Z_{1\varphi}} = {\left( {N - 1} \right) \times L_{2o} \times \gamma \times \tan^{2}\varphi}} & (14)\end{matrix}$

[0129] In this case, it is preferable that the scanning line bending inthe case where the fθ lens 61 is rotationally decenter by 8.727E-4rad(γ=8.727E-4rad) about the axis parallel to the main scanning directionis 40 μm, or preferably 20 μm or below.

[0130] Consequently, as can be seen from Equation (8), it is enough thatthe shape of each surface of the single fθ lens 61 is constructed sothat the following equation is satisfied.

|ΔZ ₁ |=|ΔZ ₁ +ΔZ ₂|≦0.040

|ΔZ ₁ |=|ΔZ ₁ +ΔZ ₂|≦0.020  (15)

[0131] If the range of Equation (15) is exceeded, there occursconspicuous image degradation due to scanning line bending. Inparticular, in a color image forming apparatus using a plurality ofscanning optical apparatuses, color drift becomes a problem.

[0132] In the scanning optical apparatus of this embodiment, thescanning line bending amount ΔZ₁ occurring in the case where θmax=±40.9(deg), ΔX₂=−12.81 (mm), L_(2o)=147.28 (mm), L_(2θ)=170.74 (mm),fs_(2o)=44.95 (mm), N=1.5242, Φ=23.7 (deg), d_(o)=17.90 (mm), _(dθ)=3.47(mm), and the single fθ lens 61 is rotationally decenter by trisection(γ=0.0008727 rad) about the axis parallel to the main scanning directionbecomes as follows from Equations (10) to (14) described above.

[0133] ΔZ₁=+0.036 (mm)

[0134] ΔZ₂=−037 (mm)

[0135] ΔZ₁=−0.00l (mm)

[0136] From these, it can be found that the single fθ lens has aconstruction satisfying Equation (15) and the sensitivity of thescanning line bending to rotational decentration is reduced.

[0137] In the scanning optical apparatus in this embodiment, the airconverted distance (actual distance/refractive index within the lens)from the deflecting surface 5 a of the polygon mirror to the exitsurface 61 b of the scanning optical element 61 on the optical axis isL_(ao)=63.193 mm, a distance from the exit surface 61 b of the scanningoptical system 61 to the surface to be scanned 8 is L_(bo)=147.283 mm,the off-axis air converted distance from the deflecting surface 5 a ofthe polygon mirror to the exit surface 61 b of the scanning opticalelement 61 is L_(aθ)=72.843 mm, the distance from the exit surface 61bof the scanning optical element 61 to the surface to be scanned 8 isL_(bθ)=170.742 mm, and the following relation is obtained.$\begin{matrix}{\frac{L_{b\quad \theta}}{L_{a\quad \theta}} = {1.0057 \times \frac{L_{bo}}{L_{ao}}}} & (a)\end{matrix}$

[0138] The main scanning direction shapes (meridional shapes) of both ofthe surfaces 61a and 61b (in particular, the exit surface 61 b) aredetermined so as to satisfy the following condition. $\begin{matrix}{{0.9 \times \frac{L_{bo}}{L_{ao}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.1 \times \frac{L_{bo}}{L_{ao}}}} & (b)\end{matrix}$

[0139]FIGS. 4A to 4C are each an aberration diagram showing paraxialaberration (the curvature of field, the curvature aberration, and themagnification difference in the sub scanning direction) of the opticalscanning apparatus in this embodiment. The solid line indicates thecurvature of field in the sub scanning direction and the dotted lineindicates the curvature of field in the main scanning direction. As canbe seen from these aberration diagrams, in this embodiment, the paraxialaberration is favorably corrected and there is realized a favorableoptical scanning apparatus suited to high-definition printing.

[0140] The ratio of Fno in the sub scanning direction becomes asfollows.

Fmin/Fmax=0.982≧0.9

[0141] This means that a certain condition concerning the sub scanningmagnification is satisfied.

[0142] When the optical path length and focal length of the scanningoptical system 61 are respectively referred to as L and f, the followingrelation is obtained.

1.35f≦L=1.45≦1.55f

[0143] This satisfies a relation between the optical path length and thefocal length that determines the shape of the exit surface in the mainscanning direction so that the sub scanning magnification is keptconstant. The relation therebetween also favorably corrects the fθcharacteristic and the curvature of field in the main scanningdirection.

[0144] When power in the sub scanning direction of entirety of thescanning optical system is referred to as Φs and power in the subscanning direction of the exit surface 61 b (second surface) is referredto as Φs2, the following relation is obtained.

0.9≦Φs2/Φs≦1.1

[0145] Power in the sub scanning direction is concentrated on the exitsurface, so that there is realized a system in which the sensitivity ofthe scanning line bending to arrangement becomes low.

[0146]FIG. 5 shows the scanning line bending in the case where theincident surface 61 a, the exit surface 61 b, and the single fθ lensitself are shifted by 50 μm in the sub scanning direction (Z direction)in the scanning optical apparatus in this embodiment.

[0147] Also, FIG. 6 shows the scanning line bending in the case wherethe incident surface 61 a, the exit surface 61 b, and the single fθ lensitself are rotationally decenter by trisection about the axis parallelto the main scanning direction in the scanning optical apparatus in thisembodiment.

[0148] As to the decentration caused by the shift in the sub scanningdirection, with the construction where the sub scanning magnification isuniformized across a lens and each surface has the identical subscanning magnification, there is suppressed the sensitivity of thescanning line bending although the height reaching the surface to bescanned varies.

[0149] Also, as to the decentration caused by the rotation about theaxis parallel to the main scanning direction, there is obtained aconstruction where Equations (10) to (15) described above are satisfiedand the shape of the incident surface 61 a is determined so that thereoccurs scanning line bending in a direction opposite to the scanningline bending caused by the rotational decentration of the exit surface61 b, with these scanning line bendings having the same bending amount.With this construction, the scanning line bending occurring on theincident surface 61 a cancels out the scanning line bending occurring onthe exit surface 6 b, which reduces the sensitivity of the scanning linebending to a small level in the case where the single fθ lens itself isrotationally decenter.

[0150] As a result, by utilizing the effects of the present invention,it becomes possible to provide a scanning optical apparatus with whichit is possible to always obtain a favorable image where the scanningline bending is suppressed to a small amount even if there occursrotational decentration.

[0151] Also, in this embodiment, in order to compensate for focusmovement with environmental change that is particularly conspicuous inthe case of a plastic lens, at least one surface of the single fθ lens61 may be formed by providing a diffraction grating surface.

[0152] Also, in this embodiment, even if the light source means isconstructed from a multi-beam laser, it is possible to apply such alight source means in the same manner as in the first embodimentdescribed above.

[0153] It does not matter whether the number of beams of the multi-beamis two or at least equal to three.

[0154] The single lens 61 that is a scanning optical element in thisembodiment may be a glass lens formed by a molding process.

[0155] Second Embodiment

[0156]FIG. 7A is a main scanning cross-sectional view of a scanningoptical apparatus in this embodiment, while FIG. 7B is a sub scanningcross-sectional view thereof.

[0157] The points of difference between this embodiment and the firstembodiment are that multi-beam is used as the light source means andthat the shapes of the incident surface and exit surface of the singlefθ lens constituting the third optical system are changed. Other aspectsare the same as those in the first embodiment.

[0158] In this drawing, reference numeral 11 denotes a multi-beam laserthat is a light source means and simultaneously emits two light fluxesthat have been modulated independently of each other (only one lightflux is shown in the drawing).

[0159] Also, in this embodiment, this scanning optical apparatus isplaced in a color image forming apparatus shown in FIG. 8. Thisapparatus is a color image apparatus in which a plurality of lightfluxes from a plurality of scanning optical apparatuses are guided ontotheir corresponding image bearing members and there is recorded imageinformation of light in different colors.

[0160]FIG. 9 shows design data in this embodiment.

[0161] In this embodiment, the incident surface 61 a of the single fθlens 61 has an aspherical shape in the main scanning direction and has aconvex toric surface in the sub scanning direction. The exit surface 61b is constructed from an aspherical shape in the main scanning directionand from a deformed toric surface in the sub scanning direction. Thisdeformed toric surface has a circular arc shape having the radius ofcurvature that is different from that in the main scanning direction.Also, the radius of curvature of the deformed toric surface varies inresponse to the main scanning direction.

[0162] As to the exit surface 61 b on which power in the sub scanningdirection is concentrated, its shape in the main scanning direction isdetermined so that there is obtained a nearly constant sub scanningmagnification within an image effective area.

[0163] When the shape is calculated using FIG. 9, there is obtained arelation of Φs2/Φs=0.932, which satisfies a condition of 0.9≦Φs2/Φs≦1.1.There is also obtained a relation of Lbθ/Laθ=0.974×Lb0/La0, whichsatisfies the following condition.${0.9 \times \frac{L_{bo}}{L_{ao}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.1 \times {\frac{L_{bo}}{L_{ao}}.}}$

[0164]FIG. 10 shows the curvatures of field in the main scanningdirection and the sub scanning direction, the fθ characteristic, and thesub scanning magnification of the single fθ lens of this embodiment,with each of these being favorably corrected.

[0165]FIG. 11 is a drawing showing the distance of a scanning line inthe sub scanning direction on a surface to be scanned in the case wherethe whole of a single fθ lens and each optical surface in thisembodiment are decenter by 50 μm in the sub scanning direction. As canbe seen from this drawing, although an irradiation position is displaceddue to the decentration, the amount of scanning line bending caused isvery small.

[0166] Also, FIG. 12 is a drawing showing the distance of a scanningline in the sub scanning direction on a surface to be scanned in thecase where the whole of the single fθ lens and each optical surface inthis embodiment are rotationally decenter by trisection about an axisparallel to the main scanning direction. As can be seen from thisdrawing, although the irradiation position is displaced due to thedecentration, the amount of scanning line bending caused is very smallin a like manner.

[0167] As described above, in this embodiment, the third optical systemis constructed from a single fθ lens constructed from a toric surfaceand a deformed toric surface. Also, there is formed an incident surfacethat satisfies the conditions expressed by Equations (10) to (15) andcauses scanning line bending in a direction opposite to scanning linebending caused by the rotational decentration of an exit surface aboutthe axis parallel to the main scanning direction, with these scanningline bendings having the same bending amount. With this construction,the scanning line bending occurring on the incident surface cancels outthe scanning line bending occurring on the exit surface, which makes itpossible to realize a scanning optical apparatus, which does not causescanning line bending in the case where a single fθ lens is rotationallydecenter, using the single fθ lens at low cost.

[0168] Further, as an effect unique to this embodiment, by uniformizingthe sub scanning magnification of a single fθ lens within an imageeffective area, there is obtained uniform intervals between scanninglines of a plurality of light fluxes on a surface to be scanned in ascanning optical apparatus using multi-beam. As a result, it becomespossible to realize a scanning optical apparatus that is capable ofperforming high-definition image formation.

[0169] Also, there is formed an incident surface that satisfies theconditions expressed by Equations (10) to (15) and causes scanning linebending in a direction opposite to scanning line bending caused by therotational decentration of an exit surface about the axis parallel tothe main scanning direction, with these scanning line bendings havingthe same bending amount. With this construction, it becomes possible torealize a color image apparatus in which there occurs no scanning linebending due to errors caused during the attachment of the single fθlens, it is not required to perform adjustment for scanning linebending, and color drift is reduced.

[0170] Third Embodiment

[0171]FIG. 13A is a cross-sectional view of a scanning optical apparatusin this embodiment in the main scanning direction, while FIG. 13B is across-sectional view thereof in the sub scanning direction. The point ofdifference between this embodiment and the first embodiment is that theshapes of the incident surface 61 a and exit surface 61 b of the singlefθ lens 61 constituting the third optical system in the sub scanningdirection are changed. Another point of difference is that the scanningoptical apparatus is placed in an image forming apparatus. Other aspectsare the same as those in the first embodiment.

[0172]FIG. 14 shows design data in this embodiment.

[0173] In this embodiment, the single fθ lens 61 has an aspherical shapein the main scanning direction and has a convex toric surface in the subscanning direction. Its exit surface has a circular arc shape in themain scanning direction and is constructed from a deformed toric surfacein the sub scanning direction that has a circular arc shape differingfrom the main scanning direction and has the radius of curvature varyingin response to the main scanning direction. The shape of the exitsurface in the main scanning direction is determined so that there isobtained a nearly constant sub scanning magnification in an imageeffective area. Also, the refracting power in the sub scanning directionis concentrated on the exit surface.

[0174]FIG. 15 shows the curvatures of field in the main scanningdirection and the sub scanning direction, the fθ characteristic, and thesub scanning magnification of the single fθ lens in this embodiment,with each of these being favorably corrected.

[0175] Here, when power of all systems of the single fθ lens in the subscanning direction is referred to as Φs and power of the exit surface onthe optical axis is referred to as Φs2, there is obtained the followingrelation.

Φs2/Φs=0.929  (16)

[0176] Also, the following condition is satisfied.

0.9≦Φs2/Φs≦1.1  (17)

[0177] There is obtained a relation of Lbθ/Laθ=1.0057×Lb0/La0 and thefollowing condition is satisfied.${0.9 \times \frac{L_{bo}}{L_{ao}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.1 \times \frac{L_{bo}}{L_{ao}}}$

[0178] In this embodiment, each of the incident surface and the exitsurface of the single fθ lens 61 has a shape in the main scanningdirection that is the same as that in the first embodiment, and theincident surface has feeble positive power in the sub scanningdirection. However, power is approximately concentrated on the exitsurface, so that the relations expressed by Conditional Equations (10)to (15) are not significantly deviated from.

[0179] If the distribution of power on the incident surface 61 a side isequal to or less than 10% of power of the whole of the single fθ lens,it is substantially possible to obtain the effects of the presentinvention. Consequently, there is obtained a shape of the incidentsurface that causes scanning line bending in a direction opposite toscanning line bending caused in the case where the exit surface 61 b isrotationally decenter about the axis parallel to the main scanningdirection, with these scanning line bendings having the same bendingamount. With this construction, there is reduced the sensitivity of thescanning line bending to the rotational decentration of the single fθlens 61 about the axis parallel to the main scanning direction.

[0180]FIG. 16 is a drawing showing the distance of a scanning line inthe sub scanning direction on a surface to be scanned in the case wherethe whole of a single fθ lens and each optical surface in thisembodiment are decenter by 50 μm in the sub scanning direction. As canbe seen from this drawing, although the irradiation position isdisplaced due to the decentration, the amount of scanning line bendingcaused is very small.

[0181] Also, FIG. 17 is a drawing showing the distance of a scanningline in the sub scanning direction in the case where the whole of asingle fθ lens and each optical surface in this embodiment arerotationally decenter by trisection about the axis parallel to the mainscanning direction.

[0182] As can be seen from this drawing, although the irradiationposition of the scanning line is displaced, the amount of scanning linebending caused is very small.

[0183]FIG. 18 is a cross-sectional view showing the main portion in thesub scanning direction showing an embodiment of an image formingapparatus of the present invention. In FIG. 18, reference numeral 104denotes an image forming apparatus. Code data Dc is inputted into thisimage forming apparatus 104 from an external device 117 such as apersonal computer. This code data Dc is converted into image data (dotdata) Di by a printer controller 111 within the apparatus. This imagedata Di is inputted into an optical scanning unit 100 having theconstruction described in the embodiments. Then, this optical scanningunit 100 emits light beam 103 modulated in accordance with the imagedata Di and a photosensitive surface of a photosensitive drum 101 isscanned by this light beam 103 in the main scanning direction.

[0184] The photosensitive drum 101 that is an electrostatic latent imagebearing member (photosensitive member) is rotated in a clockwisedirection by a motor 115. Then, in accordance with this rotation, thephotosensitive surface of the photosensitive drum 101 moves in the subscanning direction orthogonal to the main scanning direction withreference to the light beam 103. On the photosensitive drum 101, acharging roller 102 for uniformly charging the surface of thephotosensitive drum 101 is provided so as to be abutted against thesurface. Also, the light beam 103 scanned by the optical scanning unit100 is irradiated onto the surface of the photosensitive drum 101charged by the charging roller 102.

[0185] As described above, the light beam 103 has been modulated on thebasis of the image data Di and an electrostatic latent image is formedon the surface of the photosensitive drum 101 by the irradiation of thislight beam 103. This electrostatic latent image is developed as a tonerimage by a developing device 107 that is arranged so as to be abuttedagainst the photosensitive drum 101 on the downstream side in therotational direction of the photosensitive drum 101 with reference tothe irradiation position of the light beam 103.

[0186] The toner image developed by the developing device 107 istransferred onto a sheet 112 that is a material to be transferred by atransferring roller 108 arranged so as to oppose the photosensitive drum101 in the lower portion of the photosensitive drum 101. The sheet 112is contained in a sheet cassette 109 frontward of the photosensitivedrum 101 (on the right side in FIG. 18), although it is possible tomanually feed a sheet. A feed roller 110 is arranged in an end portionof the sheet cassette 109 and feeds the sheet 112 in the sheet cassette109 into a convey path.

[0187] The sheet 112, onto which an unfixed toner image has beentransferred in this manner, is further conveyed to a fixing devicearranged to follow the photosensitive drum 101 (on the left side in FIG.16). The fixing device is composed of a fixing roller 113 including afixing heater (not shown) and a pressure roller 114 that is arranged soas to be brought into pressure contact with the fixing roller 113. Withthis construction, the fixing device fixes the unfixed toner image onthe sheet 112 conveyed from the transferring unit by applying pressureand heat to the sheet 112 in a pressure contact portion between thefixing roller 113 and the pressure roller 114. Discharging rollers 116are further arranged to follow the fixing roller 113. After the tonerimage is fixed on the sheet 112, the discharging rollers 116 dischargethe sheet 112 to the outside of the image forming apparatus.

[0188] Although not shown in FIG. 16, in addition to the aforementioneddata conversion, the printer controller 111 performs control of eachcomponent (such as a motor 115) in the image forming apparatus, apolygon motor in an optical scanning unit to be described later, and thelike.

[0189]FIG. 19 is a schematic diagram showing the main part of a colorimage forming apparatus of an embodiment of the present invention. Thisembodiment relates to a color image forming apparatus of tandem typethat records image information on surfaces of photosensitive drums thatare parallel image bearing members obtained by arranging four scanningoptical apparatuses. In FIG. 19, reference numeral 60 represents a colorimage forming apparatus, each of numerals 11, 12, 13, and 14 indicates ascanning optical apparatus having the construction described in any oneof the first to third embodiments, each of numerals 21, 22, 23, and 24indicates a photosensitive drum that is an image bearing member, each ofnumerals 31, 32, 33, and 34 indicates a developing device, and numeral51 indicates a convey belt.

[0190] Respective color signals for R (red), G (green), and B (blue) areinputted into the color image forming apparatus 60 shown in FIG. 19 froman external device 52 such as a personal computer. These color signalsare converted into respective image data (dot data) for C (cyan), M(magenta), Y (yellow), and B (black) by the printer controller 53 in theapparatus. These image data are inputted into the scanning opticalapparatuses 11, 12, 13, and 14, respectively. Then, these scanningoptical apparatuses emit light beams 41, 42, 43, and 44 modulated inaccordance with respective image data, and the photosensitive surfacesof the photosensitive drums 21, 22, 23, and 24 are scanned by theselight beams in the main scanning direction.

[0191] In the color image forming apparatus in this embodiment, fourscanning optical apparatuses (11, 12, 13, and 14) are arranged so as tocorrespond to respective colors of C (cyan), M (magenta), Y (yellow),and B (black). These scanning optical apparatuses record image signals(image information) on the surfaces of the photosensitive drums (21, 22,23, and 24) in parallel. In this manner, a color image is printed athigh speed.

[0192] The color image forming apparatus in this embodiment forms latentimages in respective colors on the surfaces of their correspondingphotosensitive drums 21, 2, 23, and 24 using light beams emitted fromthe four scanning optical apparatuses 11, 12, 13, and 14 on the basis ofeach image data in the manner described above. Following this, thelatent images are transferred onto a recording material so that theselatent images are superimposed on each other. In this manner, onefull-color image is formed.

[0193] There occurs no problem even if a color image reading apparatusincluding a CCD sensor is used as the external device 52, for instance.In this case, a color digital copying machine is constructed from thiscolor image reading apparatus and the color image forming apparatus 60.

[0194] The effect of the present invention is that it becomes possibleto provide a scanning optical apparatus in which power in the subscanning direction is approximately concentrated on an exit surface andthere is used a single fθ lens whose exit surface has a shape in themain scanning direction with which the magnification in the sub scanningdirection is uniformized within an image effective area. With thisconstruction, even if the single fθ lens is rotated about an axisparallel to the main scanning direction, scanning line bending isreduced.

[0195] Also, in the case where a plurality of scanning opticalapparatuses described above are placed in a color image formingapparatus, differences in scanning line bending amount between thescanning optical apparatuses are suppressed to small amounts, whichmakes it possible to realize a color image apparatus in which it is notrequired to perform difficult adjustment for scanning line bending andcolor drift is suppressed.

What is claimed is:
 1. A scanning optical apparatus comprising: lightsource means; deflection means for deflecting a light flux emitted fromthe light source means; and a scanning optical system that images thedeflected light flux as a spot on a surface to be scanned, wherein thescanning optical system is a single lens, and wherein a surface shape ofthe single lens is set so that a direction of scanning line bending in asub scanning direction occurring when an incident surface of the singlelens is rotationally decenter about an axis parallel to a main scanningdirection is opposite to a direction of scanning line bending in the subscanning direction occurring when an exit surface of the single lens isrotationally decenter about the axis parallel to the main scanningdirection.
 2. A scanning optical apparatus according to claim 1, whereinthe scanning line bending in the sub scanning direction occurring whenthe incident surface of the single lens is rotationally decenter aboutthe axis parallel to the main scanning direction cancels out thescanning line bending in the sub scanning direction occurring when theexit surface of the single lens is rotationally decenter about the axisparallel to the main scanning direction.
 3. A scanning optical apparatusaccording to claim 1, wherein when power in the sub scanning directionof entirety of the scanning optical system is referred to as Φs andpower in the sub scanning direction of the exit surface of the singlelens is referred to as Φs2, the power in the sub scanning direction ofthe exit surface of the single lens satisfies a condition of0.9≦Φs2/Φs≦1.1.
 4. A scanning optical apparatus according to claim 1,wherein power in the sub scanning direction of an exit surface of thesingle lens satisfies a condition of 0.95≦Φs2/Φs ≦1.05.
 5. A scanningoptical apparatus according to claim 1, wherein when an air converteddistance from the deflection means to the exit surface of the singlelens on an optical axis is referred to as L_(ao), a distance from theexit surface of the single lens to the surface to be scanned is referredto as L_(bo), an off-axis air converted distance from the deflectionmeans to the exit surface of the single lens is referred to as L_(aθ),and a distance from the exit surface of the single lens to the surfaceto be scanned is referred to as L_(bθ), a shape of the exit surface ofthe single lens in the main scanning direction satisfies the followingcondition:${0.9 \times \frac{L_{bo}}{L_{ao}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.1 \times \frac{L_{bo}}{L_{ao}}}$


6. A scanning optical apparatus according to claim 4, wherein a shape ofthe exit surface of the single lens in the main scanning directionsatisfies the following condition:${0.95 \times \frac{L_{b0}}{L_{a0}}} \leq \frac{L_{b\quad \theta}}{L_{a\quad \theta}} \leq {1.05 \times \frac{L_{b0}}{L_{a0}}}$


7. A scanning optical apparatus according to claim 1, wherein a lightflux forming a linear image that is long in the main scanning directionenters the deflection means.
 8. A scanning optical apparatus accordingto claim 1, wherein the single lens is formed by a molding process.
 9. Ascanning optical apparatus according to claim 1, wherein at least one ofpower of the exit surface in the sub scanning direction and power of theincident surface in the sub scanning direction varies without anycorrelation with a shape in the main scanning direction.
 10. A scanningoptical apparatus according to claim 1, wherein a radius of curvature ofthe exit surface in the sub scanning direction varies from on the axistoward off the axis.
 11. A scanning optical apparatus according to claim1, wherein each of the incident surface and the exit surface is ananamorphotic surface.
 12. A scanning optical apparatus according toclaim 1, wherein a shape of the exit surface of the single lens iscircular arc.
 13. A scanning optical apparatus according to claim 1,wherein a shape of the exit surface of the single lens is non-circulararc.
 14. A scanning optical apparatus according to claim 1, wherein adifference between imaging magnifications in the sub scanning directionof the scanning optical system within an image effective area is 10% orless.
 15. A scanning optical apparatus according to claim 12, wherein ashape of the exit surface of the single lens in the main scanningdirection is a nearly circular arc shape having a center of curvature onthe deflection means side.
 16. A scanning optical apparatus according toclaim 1, wherein the single lens satisfies the following equations:$\begin{matrix}{{{\Delta \quad Z_{1}}} = {{{{\Delta \quad Z_{1d}} + {\Delta \quad Z_{1L}} + {\Delta \quad Z_{1\varphi}} + {\Delta \quad Z_{2}}}} \leq 0.040}} \\{{\Delta \quad Z_{2}} = {\Delta \quad X_{2} \times \frac{L_{2o}}{{fs}_{2o}} \times \gamma}} \\{{\Delta \quad Z_{1d}} = {\frac{N - 1}{N} \times \frac{1}{\cos^{2}\varphi} \times \left( {1 - \frac{L_{2o}}{{fs}_{2o}}} \right) \times \gamma \times \left( {d_{\theta} - d_{o}} \right)}} \\{{\Delta \quad Z_{1L}} = {\left( {N - 1} \right) \times \frac{1}{\cos^{2}\varphi} \times \gamma \times \left( {L_{2\theta} - L_{2o}} \right)}} \\{{\Delta \quad Z_{1\varphi}} = {\left( {N - 1} \right) \times L_{2o} \times \gamma \times \tan^{2}\varphi}}\end{matrix}$

where ΔX₂ is a deviation of a lens exit surface 6 b, Rx_(o) is adistance from the exit surface of the lens to a center of sagittalcurvature on an optical axis along a direction of the optical axis,Rx_(θ) is a distance from the exit surface of the lens to the center ofsagittal curvature at an angle of view θ along the direction of theoptical axis, L_(2o) is a distance from the exit surface of the lens tothe surface to be scanned on the optical axis, L_(2θ) is a distance fromthe exit surface of the lens to the surface to be scanned at an angle ofview θ, fs_(2o) is a focal length of the exit surface of the lens in thesub scanning direction on the optical axis, fs_(2θ) is a focal length ofthe exit surface of the lens in the sub scanning direction at the angleof view θ, N is a refractive index of the lens, d_(o) is a distancebetween the incident surface and the exit surface of the lens on theoptical axis, d_(θ) is a distance between an incident surface 6 a andthe exit surface of a lens 6 at the angle of view θ, fs_(2o) is a focallength of the exit surface of the lens in the sub scanning direction onthe optical axis, fs_(2θ) is a focal length of the exit surface of thelens in the sub scanning direction at the angle of view θ, L_(2o) is adistance from the exit surface of the lens to the surface to be scannedon the optical axis, L_(2θ) is a distance from the exit surface of thelens to the surface to be scanned at the angle of view θ, and Φ is aninclination of a ray of light after emission from the incident surfacein the main scanning direction at the angle of view θ.
 17. A scanningoptical apparatus according to claim 1, wherein the light source meansis a multi-beam light source having a plurality of light-emitting pointsthat are able to be modulated independently of each other.
 18. An imageforming apparatus comprising: a scanning optical apparatus according toany one of claims 1 to 17; a photosensitive member arranged on thesurface to be scanned; a developing device that develops anelectrostatic latent image formed on the photosensitive member by alight flux scanned by the scanning optical apparatus as a toner image; atransferring device that transfers the developed toner image onto amaterial to be transferred; and a fixing device that fixes thetransferred toner image on the material to be transferred.
 19. An imageforming apparatus comprising: a scanning optical apparatus according toany one of claims 1 to 17; and a printer controller that converts codedata inputted from an external device into an image signal and inputsthe image signal into the scanning optical apparatus.
 20. An imageforming apparatus comprising: a plurality of image bearing membersirradiated with a plurality of light flux from the scanning opticalapparatuses according to any one of claims 1 to 19 to form imagesdiffering in color one another.